<html>
<head>
	<meta charset="UTF-8">
	<meta content="IE=edge" http-equiv="X-UA-Compatible">
	<meta content="initial-scale=1.0, maximum-scale=1.0, user-scalable=no, width=device-width" name="viewport">
	<title>2679：[Usaco2012 Open]Balanced Cow Subsets </title>
	<!-- css -->
	<link href="../css/base.min.css" rel="stylesheet">
	<link href="../css/project.min.css" rel="stylesheet">
	
	<!-- favicon -->
	<!-- ... -->
</head>
<body class="page-brand">
	<header class="header header-transparent header-waterfall ui-header">
		<ul class="nav nav-list pull-left">
			<li>
				<a data-toggle="menu" href="#menu">
					<span class="icon icon-lg">menu</span>
				</a>
			</li>
		</ul>
		<a class="header-logo header-affix-hide margin-left-no margin-right-no" data-offset-top="213" data-spy="affix">[Usaco2012 Open]Balanced Cow Subsets </a>
		<span class="header-logo header-affix margin-left-no margin-right-no" data-offset-top="213" data-spy="affix">[Usaco2012 Open]Balanced Cow Subsets </span>
	</header>
	<nav aria-hidden="true" class="menu" id="menu" tabindex="-1">
		<div class="menu-scroll">
			<div class="menu-content">
				<a class="menu-logo" href="../index.html">BZOJ离线题库</a>
				<ul class="nav">
					<li>
						<a class="waves-attach" data-toggle="collapse" href="#problems">题目</a>
						<ul class="menu-collapse collapse in" id="problems">
							<li>
								<a class="waves-attach" href="../index.html">主页</a>
							</li>
							<li>
								<a class="waves-attach" href="../list.html">题目列表</a>
							</li>
						</ul>
					</li>
					<li>
						<a class="collapsed waves-attach" data-toggle="collapse" href="#about">关于</a>
						<ul class="menu-collapse collapse" id="about">
							<li>
								<a class="waves-attach" href="../about.html">关于此项目</a>
							</li>
						</ul>
					</li>
					
				</ul>
			</div>
		</div>
	</nav>
	<main class="content">
		<div class="content-header ui-content-header">
			<div class="container">
				<h1 class="content-heading">
                [Usaco2012 Open]Balanced Cow Subsets                 </h1>
                <p>时间限制：10s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：128MB</p>			</div>
		</div>
		<div class="container">
			<section class="content-inner margin-top-no">
				<div class="row">
					<div class="col-lg-13 col-md-13">
						<div class="card margin-bottom-no">
							<div class="card-main">
								<div class="card-inner">
									
                                <h3>题目描述</h3><p><div><span style="font-size: medium"><span style="color: black">Farmer John's owns N cows (2 &lt;= N &lt;= 20), where cow i produces M(i) units of milk each day (1 &lt;= M(i) &lt;= 100,000,000). FJ wants to streamline the process of milking his cows every day, so he installs a brand new milking machine in his barn. Unfortunately, the machine turns out to be far too sensitive: it only works properly if the cows on the left side of the barn have the exact same total milk output as the cows on the right side of the barn! Let us call a subset of cows &quot;balanced&quot; if it can be partitioned into two groups having equal milk output. Since only a balanced subset of cows can make the milking machine work, FJ wonders how many subsets of his N cows are balanced. Please help him compute this quantity. </span></span></div>
<p><span style="font-size: medium"><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px 宋体; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">给出</span><span lang="EN-US" xml:lang="EN-US" style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">N</span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px 宋体; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">（</span><span lang="EN-US" xml:lang="EN-US" style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">1</span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px 宋体; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">&le;</span><span lang="EN-US" xml:lang="EN-US" style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">N</span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px 宋体; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">&le;</span><span lang="EN-US" xml:lang="EN-US" style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">20</span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px 宋体; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">）个数</span><span lang="EN-US" xml:lang="EN-US" style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">M(i) (</span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px"><span lang="EN-US" xml:lang="EN-US" style="line-height: 21px; font-family: Arial; word-wrap: normal; color: black; word-break: normal">1 &lt;= M(i) &lt;= 100,000,000)</span></span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px"><span style="line-height: 21px; font-family: 宋体; word-wrap: normal; color: black; word-break: normal">，</span></span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px 宋体; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">在其中选若干个数，如果这几个数可以分成两个和相等的集合，那么方案数加</span><span lang="EN-US" xml:lang="EN-US" style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px simsun; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">1</span><span style="text-align: left; widows: 2; text-transform: none; background-color: rgb(243,248,251); text-indent: 0px; font: 14px/21px 宋体; word-wrap: normal; white-space: normal; orphans: 2; letter-spacing: normal; color: rgb(68,68,68); word-break: normal; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px">。问总方案数。</span></span></p></p><hr/><h3>输入格式</h3><p><div><span style="color: black; font-size: 14pt">&nbsp;Line 1: The integer N.&nbsp;</span></div>
<div><span style="color: black; font-size: 14pt">&nbsp;Lines 2..1+N: Line i+1 contains M(i). </span></div></p><hr/><h3>输出格式</h3><p><div><span style="color: black; font-size: 14pt">* Line 1: The number of balanced subsets of cows. </span></div></p><hr/><h3>样例输入</h3><pre>4 1 2 3 4 
INPUT DETAILS: There are 4 cows, with milk outputs 1, 2, 3, and 4. 
</pre><hr/><h3>样例输出</h3><pre> 3 
OUTPUT DETAILS: There are three balanced subsets: the subset {1,2,3}, which can be partitioned into {1,2} and {3}, the subset {1,3,4}, which can be partitioned into {1,3} and {4}, and the subset {1,2,3,4} which can be partitioned into {1,4} and {2,3}.</pre><hr/><h3>提示</h3><p>没有写明提示</p><hr/><h3>题目来源</h3><p>没有写明来源</p>
								</div>
							</div>
						</div>
					</div>
				</div>
				
				
			</section>
		</div>
	</main>

	<div class="fbtn-container">
		<div class="fbtn-inner">
			<a class="fbtn fbtn-lg fbtn-brand-accent waves-attach waves-circle waves-light waves-effect" data-toggle="dropdown" aria-expanded="true"><span class="fbtn-text fbtn-text-left">Menu</span><span class="fbtn-ori icon">apps</span><span class="fbtn-sub icon">close</span></a>
			<div class="fbtn-dropup">
				<a class="fbtn fbtn-brand waves-attach waves-circle waves-light waves-effect" href="../list.html" target="_self"><span class="fbtn-text fbtn-text-left">题目列表</span><span class="icon">menu</span></a>
				<a class="fbtn fbtn-green waves-attach waves-circle waves-effect" href="../index.html" target="_self"><span class="fbtn-text fbtn-text-left">返回主页</span><span class="icon">home</span></a>
				<a class="fbtn waves-attach waves-circle waves-effect" href="http://www.lydsy.com/JudgeOnline/submitpage.php?id=2679" target="_blank"><span class="fbtn-text fbtn-text-left">提交代码</span><span class="icon">send</span></a>
				<a class="fbtn fbtn-orange waves-attach waves-circle waves-effect" href="http://www.lydsy.com/JudgeOnline/wttl/wttl.php?pid=2679" target="_blank"><span class="fbtn-text fbtn-text-left">试题讨论</span><span class="icon">chat</span></a>
				
			</div>
		</div>
	</div>

	<!-- js -->
	<script src="../js/jquery.min.js"></script>
	<script src="../js/base.min.js"></script>
	<script src="../js/project.min.js"></script>
</body>
</html>